Conceptual Kinetic Energy and work question?

Question

A particle moving in the x direction is being acted upon by a net force F(x) = C(x^2), for some constant C. The particle moves from x initial=L to x final= 3L . What is (delta K), the change in kinetic energy of the particle during that time?
Express your answer in terms of C and L.

I keep getting this answer wrong and I have no idea why. Thanks for the help in advance guys :D

Answer 1

Remember this: Force x Distance = Work = Change in Kinetic Energy

So, if force is C x², then let dx be the distance increment, and do the definite integral from x = L to x = 3L.

∫ C x² dx from x = L to x = 3L

This comes to C (1/3) x³ from x = L to x = 3L, so the answer is:

(26/3) C L³

Answer 2

The change in kinetic energy is the same as the amount of work incurred. You should be integrating Cx^3 from L to 3L